Question
6) "Thallium 1-208 has a half-life of 3 .053 minutes. How long will it take for 120 g to decay to 7.50 grams?
Solution
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DorothyElite · Tutor for 8 years
Answer
Here's how to solve this half-life problem:<br /><br />**1. Understand the concept:** Half-life is the time it takes for half of a radioactive substance to decay. After one half-life, you'll have 50% remaining. After two half-lives, you'll have 25% remaining (half of 50%), and so on.<br /><br />**2. Determine the number of half-lives:**<br /><br />* Start: 120g<br />* After 1 half-life: 60g<br />* After 2 half-lives: 30g<br />* After 3 half-lives: 15g<br />* After 4 half-lives: 7.5g<br /><br />It takes 4 half-lives for 120g of Thallium-208 to decay to 7.5g.<br /><br />**3. Calculate the total time:**<br /><br />One half-life is 3.053 minutes. Since it takes 4 half-lives, the total time is:<br /><br />4 half-lives * 3.053 minutes/half-life = 12.212 minutes<br /><br />**Answer:** It will take 12.212 minutes for 120g of Thallium-208 to decay to 7.5g.<br />
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